Ski scooters of this kind are used both as a means of travel in connection with general sporting activities and as training equipment for cross-country skiing. As level tracks are only seldom available and cross-country movement over uneven, hilly ground is more effective and enjoyable, a braking device is essential. Most known braking devices consist of brake shoes acting on the front and/or rear wheels of the ski scooter, or of brake drums, with a brake strap, fitted to these wheels. Operation of this braking device is by hand or by the rider's foot via a rod or a pull lever. In the case of one known ski scooter brake, the braking device fitted to the rear wheel of the scooter has to be operated via a rod by means of a brake lever fitted to the foot board in front of the binding. This lever can be depressed with the tip of a ski stick. This calls for great skill and great care on the part of the rider, because this brake lever is small and unfavorably located. The rider can in consequence easily lose his balance and his safety. A further disadvantage arises from the fact that the brake lever has to be pressed downwards with the ski stick. Such a pressing movement is contrary to the natural movement with which a rider reacts when travelling downhill or if a sudden hazard is encountered.